The significant polarization components of a medium produced by contact with an electric field are first order polarization (linear polarization), second order polarization (first nonlinear polarization), and third order polarization (second nonlinear polarization). On a molecular level this can be expressed by Equation 1: EQU P=.alpha.E+.beta.E.sup.2 +.gamma.E.sup.3. . . (1)
where
P is the total induced polarization, PA1 E is the local electric field created by electromagnetic radiation, and PA1 .alpha., .beta., and .gamma. are the first, second, and third order polarizabilities, each of which is a function of molecular properties. .beta. and .gamma. are also referred to as first and second hyperpolarizabilities, respectively. The molecular level terms of Equation 1 are first order or linear polarization .alpha.E, second order or first nonlinear polarization .beta.E.sup.2, and third order or second nonlinear polarization .gamma.E.sup.3. PA1 P is the total induced polarization, PA1 E is the local electric field created by electromagnetic radiation, and PA1 .sub.X.sup.(1), .sub.X.sup.(2), and .sub.X.sup.(3) are the first, second, and third order polarization susceptibilities of the electromagnetic radiation, and .sub.X.sup.(2) and .sub.X.sup.(3) are also referred to as the first and second nonlinear polarization susceptibilities, respectively, of the transmission medium. The macromolecular level terms of Equation 2 are first order or linear polarization .sub.X.sup.(1) E, second order or first nonlinear polarization .sub.X.sup.(2) E.sup.2, and third order or second nonlinear polarization .sub.X.sup.(3) E.sup.3.
On a macromolecular level corresponding relationships can be expressed by Equation 2: EQU P=.sub.X.sup.(1) E+.sub.X.sup.(2) E.sup.2+.sub.X.sup.(3) E.sup.3. . . (2)
where
To achieve on a macromolecular level second order polarization (.sub.X.sup.(2) E.sup.2) of any significant magnitude, it is essential that the transmission medium exhibit second order (first nonlinear) polarization susceptibilities, .sub.X.sup.(2), greater than 10.sup.-9 electrostatic units (esu). To realize such values of .sub.X.sup.(2) it is necessary that the first hyperpolarizability .beta. be greater than 10.sup.-30 esu.
A significant difficulty encountered in finding suitable molecular dipoles for second order polarization effects lies in the molecular requirements that must be satisfied to achieve usefully large values of .beta.. For a molecule to exhibit values of .beta. greater than zero, it is necessary that the molecule be asymmetrical about its center, that is, noncentrosymmetric. Further, the molecule must be capable of oscillating (i.e., resonating) between an excited state and a ground state differing in polarity. It has been observed experimentally and explained by theory that large .beta. values are the result of large differences between ground and excited state dipole moments as well as large oscillator strengths (i.e., large charge transfer resonance efficiencies).
For .sub.X.sup.(2) to exhibit a usefully large value it is not only necessary that .beta. be large, but, in addition, the molecular dipoles must be aligned so as to lack inversion symmetry. The largest values of .sub.X.sup.(2) are realized when the molecular dipoles are arranged in polar alignment, e.g., the alignment obtained when molecular dipoles are placed in an electric field.
Second order polarization .sub.X.sup.(2) E.sup.2 has been suggested to be useful for a variety of purposes, including optical rectification (converting electromagnetic radiation input into a DC output), generation of an electro-optical Pockels effect (using combined electromagnetic radiation and DC inputs to alter during their application the refractive index of the medium), phase alteration of electromagnetic radiation, and parametric effects, most notably frequency doubling, also referred to as second harmonic generation (SHG).
For a number of years the materials employed for achieving second order polarization effects were noncentrosymmetric inorganic crystals, such as potassium dihydrogen phosphate and lithium niobate. Interest in nonlinear optical properties has increased in recent years, driven primarily by the emergence of optical telecommunications, but also stimulated by a broader need to raise optical manipulation capabilities closer to parity with those employed in electronics. This has resulted in an unsatisfied need for higher performance materials.
D. J. Williams, "Organic Polymeric and Non-Polymeric Materials with Large Optical Nonlinearities", Angew, Chem. Int. Ed. Engl., 1984, Vol. 23, pages 690-703, reports second order polarization susceptibilities, .sub.X.sup.(2), achieved with a variety of organic molecular dipoles. The molecular dipoles reported are comprised of an electron acceptor moiety bonded to an electron donor moiety by a linking moiety that provides a conjugated .pi. bonding system for electron transfer. Specific electron donor moieties disclosed are dimethylamino, 2- or 4-pyridyl, 2-quinolinyl, and 2-benzothiazolyl. Specific conjugated .pi. bonding systems reported are phenylene moieties. Specific electron acceptor moieties disclosed are oxo, cyano, and nitro.
J. Zyss, "Nonlinear Organic Materials for Integrated Optics", Journal of Molecular Electronics, 1985, Vol. 1, pages 25-45, discloses a variety of molecular dipole structures for nonlinear optics.
Ulman et al., U.S. Pat. No. 4,792,208, discloses organic molecular dipoles containing sulfonyl moieties as electron acceptors that have high (&gt;10.sup.-30 esu) second order hyperpolarizabilities (.beta.) and are capable of being polar aligned to produced films exhibiting high (&gt;10.sup.-9 esu) second order polarization susceptibilities (.sub.X.sup.(2)). In Robello et al., U.S. Pat. No. 5,008,043, the sulfonyl electron acceptor moieties include at least two halogen substituents on their .alpha. carbon atoms.
Robello et al., U.S. Pat. No. 4,900,127, discloses a medium exhibiting second order polarization susceptibility that is comprised of a linear vinyl polymer that contains molecular dipoles with sulfonyl electron acceptor moieties as pendant groups. Robello et al., U.S. Pat. No. 5,075,043, discloses a linear condensation polymer in which molecular dipoles containing sulfonyl electron acceptor moieties are oriented to reinforce electron displacement along the polymer backbone.
In Robello et al., U.S. Pat. No. 4,796,971, molecular dipoles forming repeating units in a crosslinked polymeric matrix are disclosed.
Dirk et at, U.S. Pat. No. 4,859,876, discloses an optical device that comprises a second order optically nonlinear element and means for providing optical input to and optical output from the element. The element comprises an organic molecule having second order optical susceptibility in an optically clear glassy polymer.